In this section we review basic facts about new non-relativistic string
action as was proposed in [1]} and that has the form
\(S=-\frac{T}{2}\int d^2\sigma \sqrt{-\tau }[\tau ^{\alpha \beta }h_{MN}+\epsilon ^{\alpha \beta }m_{MN}]\partial _\alpha x^M\partial _\beta x^N \ .\) 
